Regional Science and Urban Economics 73 (2018) 127–142

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Regional Science and Urban Economics

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Eliciting preferences for urban parks

Toke Emil Panduro a,*, Cathrine Ulla Jensen a, Thomas Hedemark Lundhede a,b,d, Kathrine von Graevenitz c, Bo Jellesmark Thorsen a,b a Department of Food and Resource Economics, Faculty of Science, University of Copenhagen, Rolighedsvej 23, 1958 Frederiksberg, Copenhagen, Denmark b Center for Macroecology, Evolution and Climate, University of Copenhagen, Rolighedsvej 23, 1958 Frederiksberg, Copenhagen, Denmark c Department of Environmental and Resource Economics, Centre for European Economic Research (ZEW), P.O. Box 103443, 68034, Mannheim, Germany d Centre for Environmental Economics and Policy in Africa, Department of Agricultural Economics, Extension and Rural Development, University of Pretoria, South Africa

ARTICLE INFO ABSTRACT

Keywords: The hedonic pricing method has been used extensively to obtain implicit prices for availability of urban green Hedonic house price model space, but few have obtained households' preference parameters. We elicit preferences and estimate willingness to Green space pay functions for park availability in Copenhagen using an approach that places identifying restrictions on the Preference heterogeneity identification utility function. We do this for two different measures of park availability and examine sources of preference heterogeneity. We find that the implicit price of another hectare of park within a 1000 m radius is 53.25 EUR per ha per year for the average apartment corresponding to an increase in annual rent of 0.33% per additional ha. For reducing distance to the nearest park by a meter, the price is 0.59 EUR per meter per year, corresponding to an increase in annual rent of 0.03‰ per meter. We apply our results to a policy scenario reducing the park area available in an area of central Copenhagen and show how estimates of aggregate welfare changes are highly sensitive to the measure of park availability applied. The findings stress the importance of paying attention to how public goods are defined when undertaking welfare economic policy analyses.

1. Introduction goods like a park. Numerous studies have used this approach to estimate the importance of green spaces and parks as more spatial data, and Parks provide recreational opportunities for urban residents and computational capacity has become available, e.g., Tyrvainen€ and visitors. Urban green spaces furthermore provide climate regulation Miettinen (2000) and Lake et al. (2000) and new applications are added functions, harbor biodiversity and provide other ecosystem services. As it regularly (e.g., Sander et al., 2010; Panduro and Veie, 2013: Franco and is a public good, the market is unlikely to provide green space in optimal Macdonald, 2018), including to value sunshine exposure in cities quantities without public intervention. Urban authorities can ensure (Fleming et al., 2018). provision through, e.g., regulation of private developers or by ensuring The hedonic price function recovered in the first stage of the hedonic themselves that land is set aside. However, in the absence of thorough method relates each attribute to the property price at the given market insights into the values of urban green space, the need for such regulation equilibrium. However, the information revealed about the preferences of may be neglected whenever new neighborhoods are planned and households is limited to their willingness to pay the implicit market price developed. for the amenity in question, and thus only welfare effects of marginal For that reason, urban and environmental economists have under- changes in an amenity can be evaluated. For amenities such as urban taken numerous studies estimating the value of urban parks and other parks, urban land use policy may sometimes cause changes that are non- green spaces to provide a better basis for the regulation of the urban marginal and discrete changes for the household. The analysis of welfare development. To that end, they have used various environmental valu- implications of discrete changes requires estimates of the households' ation techniques, notably Rosen's (1974) hedonic pricing framework, preference parameters. This crucial information can be obtained by extensively. Rosen showed how, under suitable assumptions, one can completing the second stage of the hedonic analysis outlined by Rosen obtain implicit prices of the different characteristics of a property from (1974). However, comparatively few studies have undertaken the second the hedonic price function, including the availability of various public stage and only one of these addresses the demand for urban parks

* Corresponding author. E-mail address: [email protected] (T.E. Panduro). https://doi.org/10.1016/j.regsciurbeco.2018.09.001 Received 19 January 2018; Received in revised form 5 September 2018; Accepted 5 September 2018 Available online 11 September 2018 0166-0462/© 2018 Elsevier B.V. All rights reserved. T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142

(Poudyal et al., 2009). Undoubtedly, one of the reasons for this gap in the market indicator variable to function well as an instrument. Poudyal literature is the difficulty in obtaining good instruments for handling the et al. (2009) used this approach in a second stage hedonic regression and endogeneity of the level of amenities chosen by households, resulting applied cluster techniques to identify sub-markets. Brasington and Hite from taste-based sorting. When applying multiple markets as instruments (2005) used the approach to uncover preference parameters for envi- as, e.g., Poudyal et al. (2009), spatial sorting across markets of house- ronmental qualities as well as school quality. Preferences for other urban holds is assumed not to occur, a strong and restrictive assumption in (dis-) amenities like noise have been uncovered by Day et al. (2007) many cases. In this study, we apply a different identification approach, as using a related approach based on spatially lagged implicit prices across we rely on restrictions on the utility function, an approach suggested by distances as instruments. For multiple markets within the same urban Bajari and Benkard (2005). While not perfect, their approach represents a area, it is hard to argue that no taste-based sorting takes place between simple and useful framework suited for cases like ours. It does not require markets, see, e.g., Zhang et al. (2015) for an approach specifically restrictive assumptions on sorting behavior nor on the distribution of addressing such imperfect instruments in a hedonic context. Instruments idiosyncratic taste heterogeneity making it well-suited for our study. based on household preferences for other goods are also unlikely to be The estimation of preference parameters for urban amenities and exogenous to the choice of housing. hence welfare gains and losses resulting from non-marginal changes are An alternative approach to recover preference parameters, which we sensitive to the way in which the public good attribute is measured and use, obtains identification by imposing restrictions on the utility func- modeled (Ahlfeldt, 2011). Policy evaluation should address this issue tion. This approach was first applied by Chattophadyay (1999) in an explicitly and carry out a sensitivity analysis. The literature applies a analysis of air quality in Chicago. Later Netusil et al. (2010) applied the plethora of different specifications of urban green space goods, and there same approach to study preferences for tree canopy cover in an area of is no conclusive evidence on what the most appropriate measure is in a Portland, Oregon. Bajari and Benkard (2005) expanded this framework, hedonic context. and Bajari and Kahn (2005) applied their approach to the racial We aim to further the development of the field by applying the composition of neighborhoods. Thus, the approach has been used to a alternative approach developed by Bajari and Benkard (2005), to recover very limited extent in environmental economics (von Graevenitz, 2018; preference parameters, introducing this method in the environmental Jensen et al., 2016a). economics literature on green space. Bajari and Kahn (2005) first applied A clear advantage of this approach is its transparency in contrast to it to study preferences for racial composition in neighborhoods. Earlier the instrumental variable approaches, where the necessary properties for related work by Chattophadyay (1999) uses different functional form instruments to be valid can be hard to satisfy in practice. Empirical data assumptions to identify preferences for air quality. We apply the Bajari can show substantial spatial sorting (Jensen et al., 2016a; b), with respect and Benkard (2005) approach to study preferences for urban park to preferences for green spaces, as well as a number of other possibly availability in central Copenhagen, Denmark. We decompose preference correlated preferences. Restricting sorting behavior, e.g., by using in- heterogeneity into heterogeneity related to observable struments based on market segments seems inconsistent with this socio-demographics and remaining idiosyncratic taste. We further assess observation. Furthermore, while the Bajari-Benkard approach requires the impact of using two different but commonly used park availability the analyst to restrict the shape of the utility function, it does not place measures, to investigate how sensitive estimates of the aggregate any constraints on the distribution of preferences. This property is policy-induced welfare changes and their distribution are to the specifi- especially desirable for policy analyses exploiting preference cation of the amenity in question. heterogeneity.

2. Previous work 2.2. Measures of urban green space in hedonic valuation studies 2.1. Uncovering the willingness to pay function Few fields have been as responsive to Rosen's (1974) hedonic pricing There is an abundance of studies applying GIS-based data and first framework as the environmental valuation field studying the value of stage hedonic regression techniques of varying sophistication to uncover urban green spaces. The number of studies investigating the implicit implicit prices for goods like urban parks, and only a few attempting to price of various aspects and types of urban green space is impressive, and obtain preference parameters of households or estimate demand func- we offer only a partial coverage focusing on the variation in measures of tions. The reason is that we only observe a single transaction for each urban green space availability that have been applied in the literature. All household in a typical hedonic study, and households are likely to sort of the studies, with one exception, rely solely on first stage hedonic themselves across space according to preferences. As a result, we may analysis. observe two seemingly identical households buy properties with vastly In general, most measures have focused on two aspects of supply; different amounts of the amenity, due to unobservable idiosyncratic distance to green areas and the amount of green areas. Proximity, rep- taste. As explained in detail already by Bartik (1987) and Epple (1987), resented by various distance measures from the property to one or more fitting an inverse demand curve across households is likely to result in green areas, has often been used, e.g., Lake et al. (2000) used measures of biased parameter estimates unless taste-based sorting is accounted for.1 walking distance to the nearest park in a UK study of house price de- Different approaches to tackle this issue have been suggested. The terminants, and Mansfield et al. (2005) applied various measures, first is the construction of instrumental variables through analysis of including linear distance to urban and peri-urban forest lands. The other multiple markets. When using multiple markets to create instruments, measure often applied is the amount of green area available, in either preferences are assumed to be identical across markets, conditional on absolute terms, (e.g., size of the nearest green area, area available within socio-demographics, and no sorting is assumed between markets.2 Thus, a given radius) or various relative measures of green space density within cross-market variation in prices is assumed to arise solely from differ- a radius of the property. For example, Kong et al. (2007) used density and ences in the supply of housing with different attributes. This allows a patchiness measures of urban green space in combination with distance measures. It is important to pay attention to how accessibility of amenities is 1 The literature on identifying and estimating demand schedules has grown modelled, as it affects hypothesis evaluation, as shown by, e.g. Ahlfeldt continuously; see e.g. Ekeland et al. (2004), Heckman et al. (2010), and Bishop (2011) and Sadayuki (2018), and also affects policy evaluation, as we and Timmins (2017). will show. Therefore, we evaluate the effect of specification using a 2 Ekeland et al. (2004) show conditions under which the MWTP function is measure of proximity to the nearest urban park within, a measure of the identified in a single market. total area of the urban park available, alone and in combination.

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3. Theoretical framework adopt this assumption here and discuss the sensitivity of this choice later. This leads to the following utility function: Our estimation procedure involves three steps, parallel to Bajari and X Benkard (2005) and Bajari and Kahn (2005). In the first step, we estimate U Xj; ci; γi ¼ γki log xjk þ ci (3) a hedonic house price function; in the second step, we recover k fi fi γ household-speci c preference parameters, and in the third step, we The household speci c preference parameter ik captures the intensity decompose variation in preferences using observed socioeconomic of the taste for housing good, k. With this functional form, we can rewrite characteristics. the first order condition as: A house is a composite good and can be described as a bundle of at- tributes, X , one attribute being access to green space. The price P of a γik δ πP Xj j j ¼ (4) house j in market equilibrium is a function of its attributes, PjðXjÞ. xjk δxjk Households obtain utility from consuming housing, Xj, and from all other goods described by a composite numeraire good, ci. The annual δ πP Xj fl γik ¼ xj;k (5) ow of utility for household i living in house j is described by the utility δxjk ð ; ; γ Þ γ fi function U Xj ci i where is the household speci c preference pa- δ π ð Þ t P Xj* fi rameters. Each household spends its total annual income y on housing We readily obtained the measure δ from the rst stage estima- i xjk and all other goods and occupies only one house so that i and j are tion of the hedonic price function. We directly observe xj*k, and therefore interchangeable. Utility is assumed separable in time. We can therefore γ fi can calculate ik, which is the household speci c preference parameter model the choice of housing as a static problem (Bajari and Benkard, for attribute k. Equation (4) provides the second stage hedonic estimation 3 2005). We calculate the annual cost of housing from the transaction for the willingness to pay (the marginal rate of substitution) for housing price at time of purchase. Assuming perpetual life for the house asset and good k. The preference parameter calculated in (5) for each household π multiplying the price with an asset return rate suitable for the house can be used to calculate willingness to pay for changes in amenity k. 4 π asset; we converted the price to a perpetual annuity. We set equal to Households are characterized by their demographics, d. Using these at- 5%. For comparison, the Danish Central Bank used a measure of the γ ; tributes the preference parameter, ik can be decomposed into an user-cost of housing of approximately 3% over the period, and the Danish average preference for k shared by all households, αk, and household Economic Council applied a user-cost rate of 3.7% in a study of road noise specific preferences αkd based in part on observed demographics Sid and impacts in Copenhagen (von Graevenitz, 2018). unobserved heterogeneity ωik: Households are assumed to be rational utility maximizers and choose X their preferred housing bundle given their income and preferences for lnðγikÞ¼αk þ αkdSid þ ωik (6) housing goods and all other goods. Thus, they face the following maxi- d γ fi mization problem where i captures household speci c preference pa- rameters determined by socioeconomic characteristics of the household 4. Econometric model and inherent preference heterogeneity: In the first step, we estimate the hedonic house price model using a maxU Xj; ci; γi s:t: yi ¼ πPj Xj þ ci (1) x;c Generalized Additive Model, with a gamma distribution and a logarith- mic link function (Wood, 2006). The generalized additive function is a For a housing bundle j* to be the utility maximizing choice for flexible and computationally efficient alternative to non-parametric or household i the marginal cost for house characteristic k assuming a semi-parametric models such as local linear estimation. It allows the continuous good xjk must equal the households marginal rate of substi- inclusion of a large number of covariates and utilizes splines to fita tution. The following first order conditions must hold at the optimum: flexible yet smooth functional form to the data. The data thus determine the shape of the function.6 δ U Xj ; yi πPj δxjk δ P Xj ¼ π (2) X δ U Xj ; yi πPj δci δxjk ln Pj ¼ α þ f1 Gj; S1 þ f2 tj; S2 þ f3 xj; yj; S3 þ f Xj; Sj X The right-hand side of (2) is the implicit annual price recovered from þ Zjβ Zjβ þ δh þ uj (7) the hedonic price function. The left-hand side is the household's marginal We distinguish between the variable, G, and other continuous hous- rate of substitution between the amenity and the numeraire good, which ing characteristics, X and discrete housing characteristics Z. The f func- can be interpreted as the implicit price of the good. As we only observe tions in (7) describe non-parametric smooth functions fitted using thin- one choice per household we only have one point on each indifference plate splines where S describes the basis dimensionality, i.e., the flexi- curve. Without further information about household preferences, we bility allowed in fitting the function to the data.7 Estimation of the cannot make inferences about the (non-)marginal willingness to pay. smooth functions is based on generalized cross-validation. Please see Bajari and Benkard (2005) obtain identification of household pref- Wood (2006) for a more technical description. All continuous variables erences by imposing a functional form for the utility function and assume that enter into the model are treated non-parametrically, this represented weak separability in the k housing goods.5 They suggest that one possible P in (7) by the sum over function for housing characteristics, f ðX ; S Þ. assumption for the utility function could be that the utility is logarithmic j j It is an important assumption and requirement that G, the park var- in housing goods and linear in consumption of the numeraire good. We iable, is exogenous in equation (7), and we argue that this is valid in our case. The parks in the study area have all been established a long time ago and most of them indeed date back to land uses decided upon before the 3 This assumption is obviously strong though quite standard in the hedonic literature. As the current paper examines urban green space and the supply of green space is relatively stable over time in the area under study, we believe any resulting bias to be limited. 6 While this econometric approach is attractive, our results and identification 4 Here π is set to 5%. For comparison, the Danish Central Bank used a measure does not hinge on this choice, as any flexible approach to estimating the price of the user cost of housing of approximately 3% over the period. function can be used. 5 The utility function most cut the price-function from the right angle, in other 7 The basis dimensionality was set to 5 for park variables while the other words the second order condition must hold. The concavity of the utility func- continues variables and the geographic smoothing is set automatically using tion depends on the preference parameter γik and the assumption of log utility. Generalized Cross Validation criterion.

129 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142 city developed around these areas. We explain further about this aspect considered to be either part of a different market (for very high-end below. Therefore, the decisions determining the locations of the parks properties) or reflect errors in the data, respectively. The data only included in the model are very plausibly exogenous to the households included properties bought as residential apartments by private house- making transactions in our data set. holds. Besides sales price, date of transaction and type of sale, the data Nevertheless, in all hedonic studies omitted variable bias is a concern. also include information on structural characteristics such as a number of The more recent literature addresses this concern with the use of, e.g., rooms, size of the living area, outer wall construction material and so fixed effects as discussed in Kuminoff et al. (2010). Here we control for forth. The information was extracted from the Danish Registry of omitted spatially varying variables using spatial fixed effects to capture Buildings and Housing, which contains information on all dwellings in discrete changes at neighborhood borders as well as a flexible function of Denmark. The registry also contains information on the exact location of location to capture continuously varying omitted variables as suggested each property, which allowed us to calculate several proximity variables, by von Graevenitz and Panduro (2015).In(7) the spatial fixed effect is e.g., to relevant spatial public goods, such as railway stations or shopping represented by δ, covering h school districts. The functions f2ðtj; S2Þ and possibilities for each property. We did that using R (R Core Team, 2015) f3ðxj; yj; S3Þ represent non-parametric controls for time (t) and space (x, and ArcGIS 10.2.1 (ESRI, 2011, 2015). To ensure that the analysis did not y). suffer from an edge effect all spatial externalities less than 3 km outside of the border of the housing market were included in the calculation of – 4.1. 2nd step: recovering preference parameters spatial variables see Fig. 1. The spatial data were supplied by the Danish Geodata Agency based on the kort10 database (The Danish Geodata γ Agency, 2011) and by the Danish Business Authority based on the CVR In the second step the preference parameter of each household, ik, for the k'th good is calculated based on the first order condition outlined in Registry (Danish Business Authority, 2011). (5). Specifically, we use finite differencing to recover the change in the Individual-level socioeconomic data from Statistics Denmark were predictor associated with a small change in park access. This delivers a joined with each traded apartment using coordinates. Due to the sensitive household specific estimate of the marginal willingness to pay, MWTP ; nature of individual-level socioeconomic data, these were delivered i for the good k, i.e. park proximity or density. The preference parameter spatially blurred using a raster mosaic of 100 100 m after which it was 8 bγ further refined and matched to individual properties by Geomatic A/S. estimate for this good, i, is then recovered for each household by The socio-economic data applied in the analysis is on a household level, multiplying the park variable measure for the property j, Gj* found in the observed housing choice with the asset return rate π and the marginal and their precision depends on the matching procedure applied by willingness to pay estimate. Geomatic. bγ i ¼ Gj* π ∂Pj ∂Gj* (8) 6. Study area

For (4) to hold, the good needs to be available in continuous amounts. The study area is located in the inner city area of the Danish capital, If not, then the marginal rate of substitution and the marginal cost are not Copenhagen. The study area is one of the most attractive real estate necessarily tangential to the purchased bundle. The implications would markets for apartments in Denmark. The area is characterized by high be that we cannot use (4) to recover the preference parameter for the sales prices of properties and high-income residents relative to the rest of good. Both park variables are continuous and if a household has chosen Copenhagen. The study area was selected by spatial analysis of the re- to buy the proximity or the density of parks we can use the condition in siduals from a naïve hedonic house price model for the greater Copen- (8) to estimate the preference parameter, γ . Due to the construction of ik hagen area (Lundhede et al., 2013). The residuals showed a clear pattern our park availability variables - which we explain in details below - there with areas of over- and under-prediction following distinct barriers in the may be apartments in the sample where the level of supply or access is urban landscape such as large roads, railway tracks, and large green zero. The preference parameters are unidentified for the households in spaces. The spatial distribution of the residuals indicated that the pricing these apartments, because the first order condition in (4) does not of the study area was distinctly different from the rest of Copenhagen necessarily hold at or below the kink of the censored proximity distance city. On this basis we consider the study area to be a single homogenous variable. property market for apartments. The inner city of Copenhagen includes a former industrial harbor and rd 4.2. 3 step: decomposing preference heterogeneity several recreational parks. Over the recent decades, the harbor has been transformed into a place for recreational activities. The larger recrea- In the third step, the preference parameter is regressed on observed tional parks in Copenhagen originally served other purposes, such as socioeconomic characteristics of households such as age, income, chil- defense systems, green pastures for livestock and owned by the Univer- dren and so forth, using OLS: sity of Copenhagen, the Church or the Danish Monarchy. To some extent, the parks outline the historical city limit over different historical periods XD (see Fig. 1). lnðcγik Þ¼αk þ αkdSdi þ ωik (9) d 7. Park availability variables where αk is an intercept that captures the average preference for the park α measure G, Sdi are D observed socioeconomic characteristics and kd is a We define a green space as a park only if the area has a high main- vector of parameters describing the variation that can be explained by tenance level with well-kept vegetation, and the area has to have foot- ω each observable characteristic. The parameter ki captures the house- paths making it possible to walk in the area and enjoy, e.g., small lakes, hold's residual idiosyncratic taste heterogeneity for park proximity or trees, lawns, flowers, and sports activities. This excludes, e.g., urban park density. green areas around industrial buildings and infrastructure like railroads. We apply two different measures: A simple proximity measure and a 5. Data density measure. The two measures are illustrated in Fig. 2 and follow the main strategies applied in the literature on valuation of green space using The data consists of 8880 apartments traded in central Copenhagen from the beginning of 2007 and to the end of 2011. The data include only arm length transactions. A small number of apartments traded for more 8 Summary statistics of the data applied in this study can be found in Ap- than 2,421,240 EUR or less than 13,451 EUR were removed as they were pendix A at the end of the paper.

130 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142

Fig. 1. The outline of the inner city apartment market used as a study area. Green areas mark the recreational areas coded as parks in this study.

Fig. 2. The two measures for park supply - park density (left) Fig. 2a and proximity (right) Fig. 2b. The (red) spot indicates the property, and for the distance measure, the arrow indicates the beeline distance to the nearest green area (<1000 m). On the left, the circle indicates the 1000 m radius around the same property; a circle spanning slightly more than 314 ha. the hedonic house price method. We ran a large number of different before selecting other means of transport or destinations (Jensen and models, including a number of distance or density dummies, to investi- Koch, 2004; Schipperijn et al., 2010; Toftager et al., 2011). gate the empirical spatial extent of each measure in the data. We The proximity measure is calculated from a Euclidian distance GIS compared model performances, e.g., using information criteria and sig- calculation. The degree of proximity was calculated by Xprox ¼ Ccut- nificance of parameter estimates, to obtain a set of good alternative off Xdist where Xdist describes Euclidian distance and Ccutoff is set to specifications of both variables. 1000 m. For apartments beyond this cut-off distance, the measure of Using this method, we decided on a cut-off distance of 1000 m for the proximity is set to zero. In this way, the proximity variable is easy to proximity measure. We use a flexible functional form for estimation interpret, because positive preferences for a park will result in a positive allowing the impact of increasing proximity to a park to vary within parameter. The specification reflects that the value of the service declines 1000 m of the nearest park. A distance of 1000 m corresponds to about with distance, and beyond some point will effectively be zero (Panduro 12–15 min on foot, which in previous studies has been suggested as an and Thorsen, 2014). The measure is insensitive to how large the nearest upper limit for people's willingness to travel by foot to green space, area is as well as to areas beyond 1000 m.

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Table 1 prices and increasing the distance to the coastline is associated with Summary statistics for park variables for the sample with non-zero consumption. lower prices. The pseudo-R-square is rather high (0.88), and the Log 10 Variable N Mean St. Min Max Likelihood value is similar across all models. Dev The parameter for the density measurement is significant in both the

Density measured in ha within 8487 20 19 0.002 73 models, where it appears. It can be interpreted as the implicit marginal 1000 m price of an increase in park availability of one ha within 1000 m radius of Proximity in meter to park within 8487 586 224 0.72 976 the property. It corresponds to a price premium of 66.59 EUR per ha per 1000 m year for the average apartment in the sample.11 The proximity park measure captures the distance to the closest park within 1000 m. The mean estimate for the proximity specification suggests an additional The density measure describes how many hectares of the park each property value of 1.06 EUR per meter per year for the average apartment. apartment has access to within in a cut-off value, which we decided to set When incorporating both variables in one model, we found similar esti- equal to 1000 m radius, be it any mixture of parks, e.g., several smaller mates 53.25 EUR per ha per year and 0.59 EUR per meter per year. In the parks or a single larger park. The density measure implies that the utility left tail of the distribution, where impacts are insignificant, the implicit of park supply to the household depends on the total area of parks marginal prices are all negative, which is not surprising given the smooth available within 1000 m of the property, but is insensitive to where in curves depicted in Fig. 3a–d. that radius the park is, as well as any parks further away. The two park measures are simple, commonly used measures, and 8.2. Sensitivity analysis represent two distinctly different approaches to describe the relationship between property value and parks. They furthermore operate on different Our data sets allow us to control for all observable characteristics that spatial scales with different density radius and cutoff values. The choice may be correlated with the park variables. Furthermore, to evaluate of spatial scale implies that a few households in our sample have not whether our estimates are robust to unobserved spatial variables corre- bought park availability and park proximity. As shown in Table 1,no lating with price and the variables of interest we followed the sensitivity – apartment in the sample is closer than 24 m to a park (1000 976 m) and analysis approach suggested by von Graevenitz and Panduro (2015). This those apartments situated within 1000 m from a park have a mean approach consists of re-estimating the models with different specifica- – proximity of 586 m (1000 414). The apartment with highest park den- tions designed to capture omitted variables (e.g., fixed effects) to see how sity has about 73 ha of parks within a 1000-m radius, while the mean sensitive the estimates are to assumptions made about the spatial scale of density is about 20 ha within a 1000 m radius. such omitted variables. We have applied both a spatial additive model Both park measures were calculated using Euclidian distance. How- with two-dimensional splines of varying dimensionality to fit the spatial ever, networks distance measures were also considered. In a dense urban coordinates and a standard fixed effect model based on a variety of environment such as the study area, the route choice is not obvious, and spatial entities. We found the parameters of the park availability mea- it is not clear that a network distance measure will perform better than sures to be robust across several increases in basis dimensionality for the the simple Euclidean distance. In the early analysis, the network distance spatial generalized additive model. Likewise, we found them to be stable fi measures did not perform better regarding parameter ef ciency or model across a number of spatial resolutions of the fixed effects specifications, fi t. We, therefore, chose to apply the simpler Euclidian measures. including postal codes, parishes, school districts, infrastructure spatial segmentation and finally ownership organizations for apartment build- 8. Results ings. This supports our assumption that within-school district variation in park access is exogenous. 8.1. The hedonic price function 8.3. The 2nd step: recovering preference parameters We estimated three different hedonic price models, differing only in the park variables included. The smooth functions estimated for each of Preference parameters for the park measures were recovered for all the park variables are shown in Fig. 3. The first model included only the three models. Due to the highly flexible non-parametric estimation, near density measure (Fig. 3a), the second model included only the proximity zero and slightly negative implicit prices were found for the density measure (Fig. 3b), and the third model included both measures (Fig. 3c measure at values approximately above 60 ha, while near zero and and d). The implicit prices for park density can be seen to increase at slightly negative implicit prices for the proximity measure were found different rates until 60 ha within 1000 m where after it levels off. This between 500 and 750 m in proximity. The shaded areas in the smoothing pattern can both be seen for the first model, that only contains the density plot represent 95% of expected sample prediction. Note that in these measure and the combined model that contain both park measures. The regions of negative implicit prices, the prediction area includes the value implicit price for park proximity is seen to increase until 500 m near the of zero, and these preference parameter estimates were therefore set to park. The flexible non-parametric form then allows the implicit price to zero. drop off somewhat and then it increases again to reach a maximum close As can be seen from Table 3, a total of 8880 households bought an by the park. We note that as the two variables are jointly included in the apartment in the period 2007–2011. In total 8032 households were model (Fig. 3c and d), the park proximity variable is reduced in impact found to have positive preference parameters for park density and 848 through the shape of the curves remains remarkably similar across households had a negative preference parameter, for park density, which models. we set to zero. The mean preference parameter for those 8032 house- In Table 2, we show the distribution of the estimated percentage holds from model 1 and 3 corresponds to a willingness to pay of 857 changes in the price associated with a small change in park access for EUR/year and 774 EUR/year, respectively, for their present level of parks each of the relevant park variables together with models statistics. The access relative to having no access to a park. A total of 8487 households full models include more than 40 explanatory variables9 and 8880 house had bought an apartment within 1000 m from a park while only 5274 sales. Here it suffices to say that the explanatory variables are stable and 4999 household were found to have a positive preference parameter across the three models and conform to expectations, e.g., increasing the number of rooms or the size of the living space is associated with higher 10 It should be noted that due to the use of thin plate splines the models are not exactly nested. 9 The full model is included in Appendix B. 11 Mean transaction price in the sample is 325,712 EUR (2012).

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Fig. 3. The panels describe the non-parametric smooth functions estimated for the hedonic price function for the park measures for the three model specifications (cf. equation (7)). The shapes of the curves in Fig. 3 are highly informative as they show the implicit prices for the park attributes at different levels of the amenity. The first model (3a) included only the park density measure (number of ha within 1000 m), the second model (3b) included only the proximity measure (1000 m minus distance to nearest park within 1000 m), and the third model included both density and proximity measure (3c & 3d, respectively).

Table 2 The estimated implicit prices (EUR per year per ha or meters) obtained from the hedonic regression (equation (7)) for Park Density (ha within 1000 m) and Park proximity (1000 m minus distance to nearest park within 1000 m).

Model Variable 25th percentile 50th percentile Mean 75th percentile Adj. R2 Log Likelihood

1 Density (1 ha) 27.22 61.02 66.59 98.67 0.88 107,555.74 2 Proximity (1 m) 0.76 1.02 1.06 2.55 0.88 107,560.46 3 Density (1 ha) 24.07 49.14 53.25 78.45 0.88 107,543.97 3 Proximity (1 m) 1.01 0.67 0.59 1.86 0.88 107,543.97

Note: The models include school district fixed effects and a smooth function in the spatial coordinates to control for omitted neighborhood variables. See full models in appendix. N ¼ 8880 transactions.

Table 3 Preference parameters estimated from equation (8) using each of the models from Table 2. Model 1 includes only density (hectares within 1000 m), Model 2 only proximity (1000 m minus distance to nearest park within 1000 m) and Model 3 including both. The parameter shows the households willingness to pay in EUR/year for their current park availability.

Model Variable N þ N - Mean Median SD Min Max

1 Density 8032 848 857 470 1076 0.34 16,570.45 2 Proximity 5274 3606 1396 868 1437 0.17 17,142.72 3 Density 8032 848 774 373 1020 0.18 15,123.52 3 Proximity 4999 3881 1292 646 1489 0.55 16,863.35

Note: The results are presented in EUR/year across all households. Preference parameters are only recovered for the households who bought the good. Nþ describes the number of households with a positive preference. Mean values are calculated including the households with preference parameters set to zero. N- describes the number of household with a preference parameter set to zero. for proximity calculated from model 2 and model 3, respectively. For recover their preference parameter and conservatively set it to zero. households located further away than 1000 m from a park, we cannot Households located between 500 and 750 m in proximity to a park had a

133 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142

Fig. 4. The distribution of the preference parameter (willingness to pay) for park density (left) and park proximity (right) measured in EUR/year for the households current park availability, obtained using equation (8). Fig. 4a describes the distribution of the preference parameter for Model 1 including only density (ha of park within 1000 m). Fig. 4b describes the distribution of the preference parameter calculated from Model 2 including only proximity (1000 m minus distance to nearest park). Fig. 4c describes the distribution of the preference parameter for the density of park calculated from Model 3 including both measures. Fig. 4d describes the distribution of the preference parameter for park proximity calculated from Model 3, including both measures. near zero preference parameter for marginally increasing proximity and 8.4. The 3rd step: decomposing preference variation were therefore set to zero.12 We found a mean preference parameter for model 2 and 3 corresponding to a willingness to pay of 1396 EUR/year We regressed the preference parameters obtained from Models 1, 2 and 1292 EUR/year compared with a situation of with no park in the and 3 on a number of sociodemographic variables, see Table 4. The proximity. preference parameter models in Table 4 explain about 10% of the vari- Fig. 4 shows the distribution of the recovered preference parameters ance of the calculated preference parameter. In consequence, 90% of the for the three different models. Some households have a willingness to pay preference heterogeneity among households is attributable to idiosyn- far higher than the mean, resulting in a long right tail. In other words, the cratic taste variation for park density and park proximity. The signs of the distributions reveal a large variation in taste across households where estimated parameters in the willingness to pay model largely conform to only a small proportion of the households have a very high willingness to expectations. pay. In particular for model 3, including both variables, the distribution The coefficients on the socio-economic variables are equal in size shows that a high a number of households have a near zero preference across the models estimated for the preference parameter for the prox- parameter for proximity. The distribution for the preference parameter imity models and the density models. The preferences for park density recovered using the density measure shows a wider range of values in resulted in a larger sample, which enabled a somewhat richer explana- both models. Most households have a preference parameter between tion of preference heterogeneity relative to the models based on the 0 and a 1000 EUR/year. preference parameter for proximity only. The preference intensity and willingness to pay for park availability increases with the age of the household heads. Younger households fi 12 (de ned by the oldest household member being under 30 years old) show The variation in MWTP across distances may seem puzzling. However, a weaker taste for both park proximity and park density compared to previous research by Abbott and Klaiber (2010) suggests that green space pro- households where the oldest household member is between 30 and 60. vides different amenities at different distances from a home. From e.g. a nice view for houses adjacent to green space, to recreative activities for homes On the other hand, households, where the oldest member is above 60, somewhat further away. As negative MWTP estimates are inconsistent with the show a stronger preference for density to parks. revealed preference for proximity to green space, we prefer the mechanical Car owners appear to be less willing to pay for park density, which solution of setting negative MWTP estimates to zero. A technical solution to this may reflect ease of reaching green recreational areas elsewhere. Car problem would be to impose monotonicity in the estimation. ownership also seems to affect preferences for park proximity negatively.

134 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142

Table 4 density and proximity will increase at a decreasing rate almost leveling Explaining heterogeneity in household preferences (willingness to pay in EUR/ off at high-income levels at incomes above 150,000 EUR per year for the year for current availability) for park proximity and density. Measures are ob- household member with the highest income. A similar pattern of tained from equation (8) based on a hedonic model (equation (7)) including both increasing preference intensity at a decreasing rate is found for the park measures and regressed on socio-demographics, cf. equation (9). Results are proximity models. reported for models with either proximity or density as the variable as well as for a model with both measures included combined. 9. Policy evaluation Dependent variable: Dependent variable:

Preference parameter for Preference parameter for The model estimates of the willingness to pay function above provide proximity Density the possibility to assess the welfare effects of a non-marginal change in Model 2: Model 3: Model 1: Model 3: the availability of the park good. Based on the preference parameter for Single Combined Single Combined parks, the willingness to pay for a change in park consumption can be measure measure measure measure bγ ð ð 1Þ ð 0ÞÞ; calculated as follows Gi log Gi log Gi where current proximity or Constant 5.811*** 4.890*** 5.086*** 4.812*** 0 1 density of parks is represented by Gi and Gi represents the scenario of (0.192) (0.225) (0.124) (0.118) change, e.g. a new park established or alternatively an existing park Income (1000 0.018*** 0.029*** 0.020*** 0.021*** EUR) (0.003) (0.003) (0.002) (0.002) cancelled and developed for other purposes. A scenario like the latter, Income2 0.0001*** 0.0001*** 0.00005*** 0.0001*** where a park is converted to other land-use purposes e.g. parking lots, (1000 EUR) (0.00002) (0.00002) (0.00001) (0.00001) commercial activities or apartment blocks is fictional, yet not implausible Under age 30 0.348*** 0.423*** 0.318*** 0.380*** in a dense city like Copenhagen. Like any other major city in a western (0.034) (0.040) (0.025) (0.024) Above age 60 0.030 0.150 0.274** 0.330*** European country, the pressure to convert remaining open urban spaces (0.170) (0.197) (0.131) (0.125) to other types of land-uses is high in Copenhagen given the relatively Min 5 years 0.113*** 0.018 0.100*** 0.104*** high land rent. higher (0.036) (0.043) (0.027) (0.026) To exemplify the impact of a policy intervention where an entire park education is converted to something else we calculate the welfare loss of removing Top manager 0.135*** 0.139*** 0.114*** 0.083** (0.045) (0.054) (0.034) (0.032) the romantic style and more than 150 years old Horticultural Garden Car owner 0.068 0.157** 0.259*** 0.315*** (Landbohøjskolens Have) at University of Copenhagen. The Horticultural (0.061) (0.073) (0.044) (0.042) Garden is mapped in Fig. 5 along with the catchment areas of the prox- Single 0.137 0.393** 0.232** 0.388*** imity measure and density measure. Note that The Horticultural Garden (0.164) (0.191) (0.102) (0.098) Children 0.479*** 0.839*** 0.456*** 0.592*** is located on the Frederiksberg Campus at the University of Copenhagen (0.163) (0.190) (0.100) (0.095) resulting in only few apartments located adjacent to the park. An in- Single parent 0.404** 0.677*** 0.363*** 0.511*** spection of the other parks in Copenhagen revealed that it is common to (0.167) (0.194) (0.103) (0.098) have non-residential buildings (public buildings, business, etc.) located Single above 0.717*** 0.865*** 0.443*** 0.634*** close by the parks. The Horticultural Garden is similar to other parks in age 60 (0.199) (0.232) (0.143) (0.137) Observations 5272 4993 8030 8025 Copenhagen regarding accessibility measured in proximity and avail- R2 0.089 0.111 0.106 0.128 ability measured in density. However, the Horticultural Garden is Adjusted R2 0.087 0.109 0.104 0.127 considered to be a particularly well-maintained and beautiful space and Residual Std. 1.095 1.258 1.007 0.961 the estimated welfare effects calculated here should be considered Error F Statistic 46.616*** 56.704*** 86.024*** 107.037*** appropriate for an average park in the sample area rather than this particular park. We assume that whatever the area is developed into, the < < < Note: *p 0.1; **p 0.05; ***p 0.01. new land use does not affect the values of the apartments in focus, e.g., it may be further residential building blocks. In the calculation, we account However, the parameter estimate is only significant for one of the for a possible substitution effect. proximity models. We calculated the annual welfare loss for a scenario without the Families with children are inclined to buy more park density, though Horticultural Garden for both the proximity measure and the density fi the effect is almost exactly canceled out if it is a single parent family. The measure. We based our approach on the rst stage hedonic regression parameter estimate for children based on the proximity models are both assuming that the homes transacted in the market are representative of insignificant. what the market has to offer and that people moving in have the same fi The preferences of a single person household are interesting as this is preferences as the people moving out. Thus the coef cients of the he- a fast-growing household type in many western urbanized regions, donic function, which describes the market equilibrium, were used to including Copenhagen. Our analyses reveal that being single is associated predict transaction prices for affected properties. Based on these pre- with an increase in preference intensity for park availability, except for dicted transaction prices, we calculated preference parameters for the those above 60, who had much weaker preferences as evidenced by the households according to (5) and used these predicted preferences to negative and highly significant coefficient. We find that the higher the calculate willingness to pay for the changes resulting from removing the educational attainment of the household heads, the greater the prefer- Horticultural Garden. Preference parameters calculated to be less than ence for park density. For households, with minimum one member in a zero were set to zero. top management position, we find lower preferences for both park den- The results of the calculation are presented in Table 5. The aggregated sity and park proximity. annual welfare loss was estimated to 3.72 mill. EUR/year for Model 1 From the lowest to the highest income group in the sample the including only the proximity measure, whereas the welfare loss was 3.46 preference intensity for park density increase by more than 150%. Edu- mill. EUR/year for Model 2 including only the density measure. If both cation and work position tend to correlate with income, as do also car measures were accounted for, using Model 3, the annual welfare loss was ownership and age. Having corrected for these variables, our analysis estimated to 7.08 mill. EUR/year. The difference between the welfare reveals that preferences also depend on income directly. This measure of economic calculations is a result of both the spatial extent of each mea- affluence was found to best capture the preference parameter using a sure, possible substitutions, the size of the change and its distributional fi quadratic function using the PanJen functional form ranking (Jensen and implications. In our case, it means that about ve times as many apart- Panduro, 2018). The implication is that the preference intensity for park ments would be affected when using the density measure compared to

135 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142

Fig. 5. The proximity and density catchment area around the Horticultural Garden of University of Copenhagen.

Table 5 The distribution of welfare changes from removing the Horticultural Garden, as experienced by households in the area (see Fig. 5) and measured in EUR/year. Estimates are reported for Model 1 including only a density measure (ha within 1000 m), Model 2 including only a proximity measure (1000 m – distance to nearest park) and Model 3 including both measures.

Min 1st Qu. Median Mean 3rd. Qu max N Aggregated welfare change

Model 1 Density 806.58 144 92 90 0 0 38,300 3,458,253 Model 2 Proximity 18,929 345 0 535 0 0 6960 3,726,173 Model 3 Combined 20,776 145 84 184 0 0 38,300 7,079,360

the proximity measure. The effect of the difference in distributional Table 6 impact can be seen on the mean willingness to pay between the two The distribution of the relative change in the two park measures ‘Proximity’ and measures, where the individual household's welfare loss is many times ‘Density’ from removing the Horticultural Garden for the households in the area higher for the proximity measure compared to the density measure. (see Fig. 5). The amount of park per household varies substantially across the Max 3rd Qu. Median Mean 1st. Qu Min N fi speci cations: For the density measure, the loss of the Horticultural Proximity 81 44 30 31 16 0 6960 Garden leads to a median percentage change of 5.7 for the affected Density 25.3 6.9 5.7 7.1 3.9 2.8 38,300 households (see Table 6). For the proximity measure, the change for each household is much larger with a mean loss of 30%. The non-marginal effect on individual households can be rather large Copenhagen housing stock. In this perspective, one might argue that the depending on location and choice of measurement. However, the shock hypothetical removal of the Horticultural Garden could be a non- to the Copenhagen apartment market is most likely limited. The change marginal localized event in the housing market following the definition affects less than 7000 homes, which is a very small part of the of Bartik (1988), and is unlikely to lead to, e.g., sorting effects in a short

136 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142 to medium timespan. functional form restriction may be a strong, and potentially inaccurate, The different results of the three policy evaluations stress the restriction, it may also be a (good specific) local approximation for the importance of how the relationship between parks and property price is unknown true form. We return to this below. constructed in the hedonic model, as it clearly affects the estimated The results of our second stage estimation show that parks in the inner welfare economic impact, and distribution of effects, and thus the po- city of Copenhagen provide a considerable flow of value to the residents. tential policy implications. The aggregated welfare loss and the burden Households in Copenhagen are willing to pay a considerable amount for dispersed across households differ substantially between the three he- parks, be it either proximity or high density of parks near their homes. donic specifications. Using the proximity measure approximately 6960 households share the loss, with an average lose 535 EUR/year. In the 10.3. Decomposing preference heterogeneity density case, a smaller loss of 90 EUR/year is shared by five times as many households. While in the case where the proximity and density Any policy change has distributional consequences, and drivers like measurements are combined the average loss equates to 184 EUR/year. demographic changes may imply new demands and policies. Therefore, it is of interest to policymakers and urban designers to understand patterns 10. Discussion of preference heterogeneity. We find that the socio-economic back- ground of the households can explain the preference variation to some Our main aim of this study is to enhance our insight into the value of extent. In particular, the patterns relating to families with or without urban parks applying the Bajari and Benkard (2005) framework to children and the issue of single person households are interesting. The recover and analyze preference variation for urban parks across house- growing number of single households is an urban trend, which our results holds. Our second aim was to illustrate why it is important for policy suggest could enhance the demand for urban park availability. conclusions, that researchers pay attention to the way variables measuring the urban park attribute are specified and modeled. 10.4. Policy evaluation and the choice of park availability measure

10.1. The first stage hedonic price function Our case study demonstrates that policy evaluation outcomes may hinge crucially on proper model design. Removing the park in the core of Many studies have presented first stage hedonic price functions using Copenhagen results in an aggregated total welfare loss for the neigh- various measures of park availability for urban residents. In the present boring households between 3.5 and 7 mill EUR annually, and the latter study, we applied two of the most prominent measures each in two estimate results from a model accounting for both measures of avail- separate models and combined in a joint model. These are park prox- ability. Approximately 7000 households share the aggregated loss using imity, measured as distance to nearest park and censored at 1000 m, and proximity and only those household within a distance of 1000 m are park density, which measures the area of parks available within a radius, affected whereas more than 38,000 households share the aggregated loss here 1000 m. Similar measures are used extensively in the literature (e.g., using the density variable. Clearly, for both measures, the people living Lake et al., 2000; Mansfield et al., 2005; Kong et al., 2007; Cho et al., closest to the park stand to lose the most from potential park closure. 2009; Jiao and Liu, 2010). We find that both the density and the prox- Both measures capture the households situated close to the park, but imity measures have significant explanatory power both separate and where the model using the proximity measure predicts that it is this combined, as did also Kong et al. (2007). The estimated non-parametric group who will suffer the major part of the loss, the model using the relationship between price and the park measures recover a meaningful density measure also includes smaller losses to a wider group of people functional form. The proximity measure depicts a relationship where the including those living further away. marginal willingness to pay increase until 500-m proximity, then levels On a strategic level, the two park measures could result in different off somewhat and increases again at about 200 m. Our functional form policy strategies being developed. Focusing on proximity measures could for accessibility is more flexible in some ways than those used by, e.g., lead to a strategy of many smaller parks, as aggregate area is ignored. The Lake et al. (2000) and Mansfield et al. (2005). The marginal willingness opposite could be true if the density measurement is the only focus, as to pay for park density increases up to the point of about 60 ha after proximity is ignored. The key goal would be to ensure as high a level of which it levels off. This suggests the existence of a saturation point where park availability as measured by the density measure, for the lowest cost. the amount of park in an area does not add additional value to In this paper, we find that the proximity measure and the density mea- households. sure do not compete but are complementary in the description of the We find that both the proximity and the density measure can be marginal willingness to pay for urban parks. Therefore, the better strat- included within the same model, suggesting they capture different as- egy to would be to strike a balance between proximity and density in the pects of urban park availability. To exclude one or the other park measure preservation and development of parks in an urban area. in an analysis would lead to a situation where not all attributes are accounted for. We initially estimated the models using a parametric 10.5. Caveats approach where we found that both measures in the same model lead to insignificant estimates of the park proximity. This finding underlines the There are specific and general caveats in the approach and results superiority of the non-parametric approach adopted in the paper. The presented in this paper worth mentioning. First, we note that our dataset more general model is to be preferred as it captures more dimensions of describing sociodemographic variables for all households are related to the amenity. the residents in the last year of our cross section, 2011. Using coordinates of dwellings, these were joined with all sales in the period 2007–2011. 10.2. The second stage: recovering preference parameters We essentially assume that the new residents are moving to the area in the period 2007–2011 have the same observed socioeconomic charac- There are very few second stage hedonic price studies in the envi- teristics as those who are already living in the area – or at least that the ronmental economics literature altogether, and in fact, only one which socio-demographic mean parameters of the 100 100 m fitted mean has addressed the demand for urban parks, namely Poudyal et al. (2009). estimates were constant over the period. This might not be the case, but Part of the explanation for this is likely the challenges of setting up a valid on the other hand, we have no reason to believe that the composition of identification strategy. Here, we introduce to the field a transparent people has changed substantially during the relatively short period. identification strategy based on functional form assumptions, which was A second general caveat of the hedonic method, which is also true for suggested and applied by Bajari and Benkard (2005) and has been later our application here, is, that when using the hedonic method for a policy applied by Bajari and Kahn (2005) and von Graevenitz (2018). While the change like the one evaluated, we only include the welfare effects of

137 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142 people living in the neighborhood. People further away, including the economics. A fairly large number of studies have estimated hedonic price more than 1500 university employees and 4000 students on that part of functions for parks, other green areas, trees and similar goods and it is the campus, who visit the Horticultural Garden or who have other bonds likely that this literature of applied environmental economics will to the garden may also experience welfare effects. These are not continue to grow and increase the evidence for the obvious values of accounted for in any hedonic analysis. urban parks and green spaces. We also note that the welfare economic loss here does not include However, there is an unfortunate shortage of studies addressing the attention to property taxes. As noted by Anthon et al. (2005) and Zhou estimation of demand for urban parks and green spaces; that is suc- et al. (2013), property owners in Denmark pay property taxes based on ceeding in estimating the so-called second stage of the hedonic model the market value of their property. This imply that any change in value – framework. upward or downward – also affects expected tax payments. Housing In this study, we obtain new insights into the preferences for and market prices reflects this. Thus, our estimated loss here is a conservative value of urban parks by applying a framework suggested by Bajari and measure of the true loss as it only captures the net loss for households and Benkard (2005), where identification of preferences rely on functional not the effect of reduced property taxes. form restrictions on the utility function. Second, we demonstrated how The Bajari and Benkard (2005) approach is subject to criticism. The urban parks provide non-negligible flows of value and that preferences functional form restriction may be a strong and potentially inaccurate for park availability vary with socio-demographics in ways that may have restriction. However, we view the chosen functional form as a (reason- interesting policy implications. Thirdly, using two standard measures of able specific) local approximation for the unknown true form. This park availability, we demonstrated just how critical a proper choice of identification strategy does not require restrictions on preference het- such measures is for the policy evaluation outcome. erogeneity nor does it require assumptions about sorting behavior. We have chosen a simple functional form due to its useful properties and Acknowledgment avoided assumptions on preference heterogeneity. It represents a local approximation to the unknown true functional form. Strong assumptions This paper benefited from the project ”Benefits from investing in concerning the unknown distribution of preference heterogeneity are urban life and urban qualities.” funded in a collaboration between the common elsewhere in the consumption literature, e.g., in the Random municipalities of Aarhus, Albertslund, Brøndby, Frederiksberg, Gladsaxe, Utility Model framework (McFadden, 1973). In our study, where pref- Glostrup, Herlev, Hvidovre, Ishøj, Københavns, Lyngby-Taarbæk, erence heterogeneity is in focus, an approach requiring restrictions on Rødovre, Skanderborg, and Vallensbæk and the Capital Region of preferences along this dimension would not be suitable. Denmark, the Ministry of Environment and Food, the developers Kil- debjerg Ry A/S, By & Havn I/S and the University of Copenhagen. 11. Concluding remarks Thorsen and Lundhede further acknowledge funding from the Danish National Research Foundation (DNRF No. 96) for the Center for Macro- The value of urban parks and green space for urban residents ecology, Evolution, and Climate. continuously attracts the interest of many types of research, including

Appendix A. Descriptive statistics and variable explanation

Appendix A.1

The Appendix contains a description of the variables used in the hedonic price function and in the preference heterogeneity analysis. Table A.1 Description of variables in the hedonic price function.

Name of variable Description

Price The transaction price of the property in EUR. Time The analysis period measured in days starting from January 1st, 2007 to December 31st, 2011. x The x coordinate measured in UTM 32 North WGS 1984 y The y coordinate measured in UTM 32 North WGS 1984 Size The size of the living area in square meters. Room The number of rooms in the apartment. Built after 2000 Dummy variable that describes whether the apartment building was built after 2000. 1 corresponds to being built after 2000 and 0 corresponds to being built before 2000. Built between 1980 and Dummy variable that describes whether the apartment building was built between 1980 and 1999. 1 corresponds to being built between 1975 and 1999 1999 and 0 corresponds to not being built between 1980 and 1999. Built between 1948 and Dummy variable that describes whether the apartment building was built between 1948 and 1979. 1 corresponds to being built between 1948 and 1979 1979 and 0 corresponds to not being built between 1948 and 1979. Built between 1947 and Dummy variable that describes whether the apartment building was built between 1910 and 1947. 1 corresponds to being built between 1910 and 1947 1910 and 0 corresponds to not being built between 1910 and 1947. Built between 1909 and Dummy variable that describes whether the apartment building was built between 1875 and 1909. 1 corresponds to being built between 1875 and 1909 1875 and 0 corresponds to not being built between 1875 and 1909. Tile roof Dummy variable that describes whether the roof is made of tile. 1 corresponds to being built of tile and 0 corresponds to not made of tile. Cement roof Dummy variable that describes whether the roof is made of cement. 1 corresponds to being built of cement and 0 corresponds to not made of cement. Felt roof Dummy variable that describes whether the roof is a felt roof. 1 corresponds to being a felt roof and 0 corresponds to not being a felt roof. Fiber board roof Dummy variable that describes whether the roof is made of fiberboard. 1 corresponds to being made of fiber board and 0 corresponds to not made of fiber board. Flat Fiber board roof Dummy variable that describes whether the roof is a flat fiber board roof. 1 corresponds to being a flat fiber board and 0 corresponds to not being a flat fiber board. Renovation 1980s Dummy variable that describes whether the apartment has undergone major renovation during the 1980s. 1 corresponds to major renovations and 0 corresponds to no major. Renovation 1990s Dummy variable that describes whether the apartment has undergone major renovation during the 1990s. 1 corresponds to major renovations 0 corresponds to no major renovation. (continued on next column)

138 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142

Table A.1 (continued )

Name of variable Description

Renovation 2000s Dummy variable that describes whether the apartment has undergone major renovation during the 2000s before the apartment is sold. 1 corresponds to major renovations and 0 corresponds to no major renovation. Number of buildings The number of buildings in the apartment complex. Number of units The number of apartment units in the apartment complex. Large Road Proximity to the nearest large road described on a scale from 0 to 200 m where 0 corresponds to a distance of 200 m and 200 corresponds to being located directly on the large road. Railway track Proximity to the nearest railway track described on a scale from 0 to 200 m where 0 corresponds to a distance of 200 m and 200 corresponds to being located on the railway track. Traffic noise >75 dB Dummy variable that describes whether the apartment is located in an area where the average traffic during the day is above 75 dB. 1 corresponds to being located in a traffic noise zone above 75 dB and 0 corresponds to not to being located in a traffic noise zone above 75 dB. Traffic noise 70–74 dB Dummy variable that describes whether the apartment is located in an area where the average traffic during the day is between 70 and 74 dB. 1 corresponds to being located in a traffic noise zone between 70 and 74 dB and 0 corresponds to not to being located in a traffic noise zone between 70 and 74 dB Traffic noise 65–69 dB Dummy variable that describes whether the apartment is located in an area where the average traffic during the day is above 75 dB. 1 corresponds to being located in a traffic noise zone above 75 dB and 0 corresponds to not to being located in a traffic noise zone above 75 dB. Traffic noise 60–64 dB Dummy variable that describes whether the apartment is located in an area where the average traffic during the day is above 75 dB. 1 corresponds to being located in a traffic noise zone above 75 dB and 0 corresponds to not to being located in a traffic noise zone above 75 dB. Coastline Proximity to the nearest coastline described on a scale from 0 to 300 m where 0 corresponds to a distance of 300 m and 300 corresponds to being located directly on the coastline. Number of shopping Number of shopping possibilities within a 1000 m walking radius possibilities Diversity of shopping The diversity of shopping possibilities within a 1000 m walking radius possibility Number of rental apartments The number of rental apartments within a 1000 m walking radius Number of residents The number of residents within a 1000 m walking radius Park density The number of hectares within a 1000 m beeline distance Park proximity Proximity to the nearest park described on a scale from 0 to 400 m where 0 corresponds to being at a distance of 400 m and 400 corresponds to being located on the border of the park

Table A.2 Summary statistics of the variables in the apartment model.

Variable Mean St. Dev. Min Max

Size 91.67117 35.71755 32 401 Room 3.03153 1.14267 1 10 Built after 2000 0.15827 0.36501 0 1 Built between 1980 and 1999 0.02402 0.15312 0 1 Built between 1948 and 1979 0.18679 0.38976 0 1 Built between 1947 and 1910 0.21242 0.40904 0 1 Built between 1909 and 1875 0.35363 0.47812 0 1 Tile roof 0.29809 0.45744 0 1 Cement roof 0.01469 0.12032 0 1 Felt roof 0.31954 0.46632 0 1 Fiber board roof 0.14293 0.35002 0 1 Flat Fiber board roof 0.14615 0.35328 0 1 Bathroom 1.026 0.23945 0 3 Renovation 1980s 0.01823 0.13378 0 1 Renovation 1990s 0.03463 0.18286 0 1 Renovation 2000s 0.03549 0.18503 0 1 Number of buildings 1.79583 10.10624 1 242 Number of units 44.64065 50.92139 1 253 Large Road 34.206 58.095 0 190.210 Railway track 12.262 36.154 0 18.639 Park proximity 1.377 1.474 0 4.760 Park density 19.583 19.00.5 0 73.844 Time 728.375 43.751.250 0 1.460 Traffic noise >75 dB 0.00397 0.06287 0 1 Traffic noise 70–74 dB 0.04643 0.21042 0 1 Traffic noise 65–69 dB 0.09457 0.29264 0 1 Traffic noise 60–64 dB 0.21231 0.40896 0 1 Coast line 4.184.109 8.474.363 0 297.317 Number of shopping possibilities 56.698960 38.206080 10 2209 Diversity of shopping possibility 47.423 1.056726 7 57 Number of rental apartments 968.499 70.018290 0 2613.345 Number of residents 19,146.630 9858.619 0 41,543 Note: N ¼ 8880.

139 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142

Table A.3 Summary statistics of the fixed effect school districts in the model.

Fixed effect

School district Mean St. Dev. Min Max

Amager Fælled Skole 0.02809 0.16525 0 1 Christianshavns Skole 0.04504 0.20739 0 1 Den Classenske Legatskole 0.03817 0.19162 0 1 Gasværksvejens Skole 0.00804 0.08932 0 1 Guldberg Skole 0.03238 0.17702 0 1 Heibergskolen 0.00836 0.09107 0 1 Kildevældsskolen 0.04171 0.19994 0 1 Klostervængets Skole 0.01222 0.10989 0 1 Langelinieskolen 0.04986 0.21767 0 1 Lindevangskolen 0.05061 0.21921 0 1 Lundehusskolen 0.01330 0.11455 0 1 Ny Hollænderskolen 0.05672 0.23133 0 1 Nyboder Skole 0.02616 0.15963 0 1 Oehlenschlægersgades Skole 0.02295 0.14974 0 1 Randersgades Skole 0.02766 0.16402 0 1 Skole ved Søerne 0.02241 0.14802 0 1 Skolen i Sydhavnen 0.05243 0.22291 0 1 Skolen på Duevej 0.04568 0.20880 0 1 Skolen på Islands Brygge 0.04589 0.20926 0 1 Skolen på la Cours Vej 0.03067 0.17242 0 1 Skolen på Nyelandsvej 0.04579 0.20903 0 1 Skolen ved Bulowsvej 0.04954 0.21700 0 1 Sortedamskolen 0.01072 0.10300 0 1 Strandvejsskolen 0.03163 0.17503 0 1 Sølvgades Skole 0.02992 0.17037 0 1 Søndermarkskolen 0.02606 0.15931 0 1 Tove Ditlevsens Skole 0.02209 0.14698 0 1 Valby Skole 0.00558 0.07447 0 1 Vesterbro Ny Skole 0.02262 0.14871 0 1 Vibenshus Skole 0.05662 0.23112 0 1 Øster Farimagsgades Skole 0.01909 0.13684 0 1 Ålholm Skole 0.00043 0.02071 0 1 Note: N ¼ 8880.

Table A.4 Variable description of the socio-economic variables used in the willingness to pay function.

Name of variable Description

Income (in 1000 EUR) Measure the income of the highest earning person in the household measured in steps of 1000 EUR. Min 5 years higher The adults in the household have minimum 5 years of education. The variable is constructed as a dummy variable which equals 1 when they have education minimum 5 years of education and 0 Otherwise. Top manager The occupation of a member of the household is top manager. The variable is constructed as a dummy variable where 1 equals having a top manager in the household and 0 equals not having a top manager in the household. Car owner The household own a car. The variable is constructed as a dummy variable where 1 equals having a car and 0 equals having no car. Single The household have only one adult. The variable is constructed as a dummy variable where 1 equals having only one adult in the household and 0 equals having more than one adult in the household. Children The household have one or more children. The variable is constructed as a dummy variable where 1 equals having one or more children in the household and 0 equals having no children in the household. Under age 30a) The oldest member of the household is under 30 years of age. The variable is constructed as a dummy variable where 1 equals having no adults above 30 years age in the household and 0 equals having at least one adult over 30 years of age in the household. Above age 60b) The oldest member of the household is above 60 years of age. The variable is constructed as a dummy variable where 1 equals having at least one adult above 60 years age in the household and 0 equals having zero adults over 60 years of age in the household.

Table A.5 Summary statistics of the socio-economic variables used in willingness to pay function.

Variable Mean St. Dev. Min Max

Income (in 1.000 EUR) 57.77367 22.52489 17.86070 199.42330 Min 5 years higher education 0.51212 0.49988 0 1 Top manager 0.29466 0.45591 0 1 Car owner 0.18186 0.38575 0 1 Single 0.76968 0.42106 0 1 Children 0.70963 0.45396 0 1 Under age 30a 0.36414 0.48121 0 1 Above age 60b 0.04321 0.20335 0 1 Note: N ¼ 8880. a For 481 households the age of the oldest member of the household is only known to be less than 50 and for 268 households the age is only known to be less than 60. We assume the age to be minimum 30. b For 189 households the age of the oldest member of the household is only known to be above 40 and we assume the age to be less than 61.

140 T.E. Panduro et al. Regional Science and Urban Economics 73 (2018) 127–142

Appendix B. First stage model results

First stage - results

log (house price)

Density Proximity Combined

Tile roof 0.00867 0.01649** 0.01082 (0.00831) (0.00832) (0.00833) Cement roof 0.04616*** 0.05482*** 0.04681*** (0.01680) (0.01680) (0.01680) Fiber board roof 0.01279 0.01932** 0.01394* (0.00815) (0.00815) (0.00816) Board roof 0.01172 0.01874** 0.01295 (0.00860) (0.00858) (0.00864) Flat roof 0.03521*** 0.04036*** 0.03666*** (0.00882) (0.00885) (0.00884) Bathrooms 0.07077*** 0.06834*** 0.06992*** (0.00779) (0.00779) (0.00779) Renovated in 1980s 0.00915 0.00834 0.01063 (0.01308) (0.01309) (0.01308) Renovated in 1990s 0.03508*** 0.03809*** 0.03537*** (0.00956) (0.00955) (0.00956) Renovated in 2000s 0.07228*** 0.07543*** 0.07497*** (0.00911) (0.00914) (0.00914) Noise level 1 0.03737 0.03964 0.03785 (0.02742) (0.02741) (0.02737) Noise level 2 0.04040*** 0.04146*** 0.04018*** (0.00832) (0.00833) (0.00833) Noise level 3 0.02381*** 0.02355*** 0.02416*** (0.00606) (0.00609) (0.00608) Noise level 4 0.01331*** 0.01433*** 0.01362*** (0.00418) (0.00419) (0.00419) Square meters df ¼ 7.5*** df ¼ 8.2*** df ¼ 8.5*** Number of floors df ¼ 6.9*** df ¼ 7.7*** df ¼ 7.7*** Age of building df ¼ 8.6*** df ¼ 9.0*** df ¼ 9.0*** Number of rooms df ¼ 4.7*** df ¼ 5.7*** df ¼ 5.7*** Number of buildings in the housing unit df ¼ 1.0*** df ¼ 1.0*** df ¼ 1.0*** Number of apartments in the building df ¼ 8.5*** df ¼ 8.9*** df ¼ 8.9*** Proximity to big road (censored at 200 m) df ¼ 5.8*** df ¼ 6.2*** df ¼ 6.5*** Proximity to railway tracks (censored at 200 m) df ¼ 8.9*** df ¼ 9.0*** df ¼ 8.9*** Proximity coastline (censored at 300 m) df ¼ 5.2*** df ¼ 5.4*** df ¼ 5.4*** Number of services within 1000 m df ¼ 8.1* df ¼ 7.9* df ¼ 8.0 Diversity of services within 1000 m df ¼ 8.9*** df ¼ 9.0*** df ¼ 9.0*** Number of children in nearest daycare center df ¼ 8.8*** df ¼ 8.9*** df ¼ 8.7*** Number of rental apartments within 1000 m df ¼ 8.9* df ¼ 8.8*** df ¼ 9.0*** Number of residence within 1000 m df ¼ 8.2*** df ¼ 9.0*** df ¼ 8.6* Numeric vector describing time of sale df ¼ 8.9*** df ¼ 8.9*** df ¼ 8.9*** Geografical coordinates (x,y) df ¼ 28*** df ¼ 27.8*** df ¼ 28.1*** Park density df ¼ 4.0*** df ¼ 3.6*** Park proximity df ¼ 3.7*** df ¼ 3.9*** Constant 12.49922*** 12.50662*** 12.49852*** (0.02520) (0.02522) (0.02546) Adjusted R2 0.87971 0.87935 0.87999 Log Likelihood 107,736.10000 107,747.90000 107,728.30000 UBRE 0.02178 0.02184 0.02174 Notes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05.

Appendix C. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.regsciurbeco.2018.09.001.

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